Reconsider the system defect situation described in Exercise 26 (Section 2.2). a. G...

Reconsider the system defect situation described in Exercise 26 (Section 2.2).

a. Given that the system has a type 1 defect, what is the probability that it has a type 2 defect?

b. Given that the system has a type 1 defect, what is the probability that it has all three types of defects?

c. Given that the system has at least one type of defect, what is the probability that it has exactly one type of defect?

d. Given that the system has both of the first two types of defects, what is the probability that it does not have the third type of defect?

Reference exercise- 26

A certain system can experience three different types of defects. Let A_i(i= 1,2,3) denote the event that the system has a defect of type i. Suppose that

P(A₁)= .12 P(A₂) = .07 P(A₃) =.05

P(A₁ ∪A₂)= .13 P(A₁ ∪A₃)= .14

P(A₂ ∪A₃) = .10 P(A₁ ∩A₂ ∩A₃) = .01